diff --git a/crates/calc/src/eval/call.rs b/crates/calc/src/eval/call.rs
index 8ac58c8d1..848762ab9 100644
--- a/crates/calc/src/eval/call.rs
+++ b/crates/calc/src/eval/call.rs
@@ -203,9 +203,9 @@ impl<'h> Evaluator<'h> {
         let index = self.value(&args[0]);
         if let Value::Array(_) = index {
             let Some(spec) = gridcraft_functions::lookup("CHOOSE") else { return err(CellError::Name) };
-            let mut evaluated = vec![Arg { value: index, from_ref: false }];
+            let mut evaluated = vec![Arg::val(index)];
             for argument in &args[1..] {
-                evaluated.push(Arg { value: self.value(argument), from_ref: false });
+                evaluated.push(Arg::val(self.value(argument)));
             }
             let mut context = FnCtx { ev: self, criteria: None, lambda: None };
             return gridcraft_functions::call(spec, &evaluated, &mut context).pipe(Ev::V);
@@ -351,7 +351,9 @@ impl<'h> Evaluator<'h> {
                 }
                 ev => self.deref(ev),
             };
-            evaluated.push(Arg { value, from_ref });
+            // Only an argument left out (`f(a,,b)`) is omitted; one that computes a blank is given.
+            let blank_value = !from_ref && value == Value::Empty && lambda_at != Some(i) && !matches!(a, Expr::Missing);
+            evaluated.push(Arg { value, from_ref, blank_value });
         }
         let mut ctx = FnCtx { ev: self, criteria, lambda };
         gridcraft_functions::call(spec, &evaluated, &mut ctx).pipe(Ev::V)
@@ -414,7 +416,7 @@ impl<'h> Evaluator<'h> {
         let (Some(sum), Some(count)) = (gridcraft_functions::lookup("SUM"), gridcraft_functions::lookup("COUNT")) else {
             return Err(err(CellError::Name));
         };
-        let args = [Arg { value, from_ref }];
+        let args = [Arg { value, from_ref, blank_value: false }];
         if kind != Agg::Count {
             match gridcraft_functions::call(sum, &args, &mut FnCtx { ev: self, criteria: None, lambda: None }) {
                 Value::Number(n) => acc.sum += n,
diff --git a/crates/calc/src/eval/reference_fns.rs b/crates/calc/src/eval/reference_fns.rs
index 4f5154c2d..6bef99732 100644
--- a/crates/calc/src/eval/reference_fns.rs
+++ b/crates/calc/src/eval/reference_fns.rs
@@ -203,7 +203,7 @@ impl<'h> Evaluator<'h> {
             let horizontal = l.range.height() == 1 && l.range.width() > 1;
             let same_len = if vertical { r.range.height() == l.range.height() } else { r.range.width() == l.range.width() };
             if !matches!(key, Value::Array(_)) && (vertical || horizontal) && same_len {
-                let mut xargs = vec![Arg { value: key, from_ref: false }, Arg { value: self.area_value(&l), from_ref: true }];
+                let mut xargs = vec![Arg::val(key), Arg::reference(self.area_value(&l))];
                 // An empty match_mode before a given search_mode is the default (0), not the end.
                 let given = |i: usize| args.get(i).is_some_and(|e| !matches!(e, Expr::Missing));
                 let last = if given(5) {
@@ -215,10 +215,11 @@ impl<'h> Evaluator<'h> {
                 };
                 for i in 4..=last {
                     match args.get(i) {
-                        Some(Expr::Missing) | None => xargs.push(Arg { value: Value::Number(0.0), from_ref: false }),
+                        Some(Expr::Missing) | None => xargs.push(Arg::val(Value::Number(0.0))),
                         Some(e) => {
                             let value = self.value(e);
-                            xargs.push(Arg { value, from_ref: false });
+                            let blank_value = value == Value::Empty;
+                            xargs.push(Arg { value, from_ref: false, blank_value });
                         }
                     }
                 }
diff --git a/crates/calc/src/tests.rs b/crates/calc/src/tests.rs
index fffbc59a1..3c1330dbe 100644
--- a/crates/calc/src/tests.rs
+++ b/crates/calc/src/tests.rs
@@ -1842,6 +1842,9 @@ fn lookup_of_an_empty_cell_stays_blank() {
         ("D8", "=VLOOKUP(\"k\",A1:B2,2,0)", Value::Number(0.0)),
         // Arithmetic still reads the blank as 0.
         ("D9", "=VLOOKUP(\"k\",A1:B2,2,0)+1", Value::Number(1.0)),
+        // A blank lookup given as an argument is still given, not omitted.
+        ("D10", "=FILTER(1,FALSE,VLOOKUP(\"k\",A1:B2,2,FALSE))", Value::Number(0.0)),
+        ("D11", "=XLOOKUP(\"z\",A1:A2,B1:B2,VLOOKUP(\"k\",A1:B2,2,0))", Value::Number(0.0)),
     ] {
         t.set(at, f);
         assert_eq!(t.get(at), want, "{f}");
diff --git a/crates/functions/src/info.rs b/crates/functions/src/info.rs
index 309f0323e..82eda5828 100644
--- a/crates/functions/src/info.rs
+++ b/crates/functions/src/info.rs
@@ -91,7 +91,7 @@ fn na(_a: &[Arg], _c: &mut dyn Ctx) -> R<Value> {
 fn n_fn(a: &[Arg], _c: &mut dyn Ctx) -> R<Value> {
     // N(range) reads the range's first cell, but a computed array (N(A1:A3>0), N({...})) is
     // converted element by element, so N can stand in for `--` inside SUMPRODUCT.
-    if let Some(Arg { value: Value::Array(arr), from_ref: false }) = a.first() {
+    if let Some(Arg { value: Value::Array(arr), from_ref: false, .. }) = a.first() {
         let data = arr.data.iter().map(|v| n_of(v.clone()).unwrap_or_else(Value::Error)).collect();
         return Array::new(arr.rows, arr.cols, data).map(Value::from).ok_or(CellError::Calc);
     }
diff --git a/crates/functions/src/lib.rs b/crates/functions/src/lib.rs
index ccc61b026..6cb035b28 100644
--- a/crates/functions/src/lib.rs
+++ b/crates/functions/src/lib.rs
@@ -87,16 +87,19 @@ pub use stat::{aggregate_values, aggregate_values_k};
 pub struct Arg {
     pub value: Value,
     pub from_ref: bool,
+    /// A written argument whose value came out blank (a lookup of an empty cell): given, not
+    /// omitted, although its value is `Value::Empty`.
+    pub blank_value: bool,
 }
 
 impl Arg {
     /// A literal (non-reference) argument.
     pub fn val(value: impl Into<Value>) -> Arg {
-        Arg { value: value.into(), from_ref: false }
+        Arg { value: value.into(), from_ref: false, blank_value: false }
     }
     /// An argument that came from a cell or range reference.
     pub fn reference(value: impl Into<Value>) -> Arg {
-        Arg { value: value.into(), from_ref: true }
+        Arg { value: value.into(), from_ref: true, blank_value: false }
     }
 }
 
diff --git a/crates/functions/src/lift.rs b/crates/functions/src/lift.rs
index ea7f07fd9..6d2e3fbc4 100644
--- a/crates/functions/src/lift.rs
+++ b/crates/functions/src/lift.rs
@@ -50,12 +50,7 @@ fn reject_multi_cell_refs(spec: &FnSpec, args: &[Arg]) -> Option<Vec<Arg>> {
     if !args.iter().enumerate().any(|(i, a)| multi(i, a)) {
         return None;
     }
-    Some(
-        args.iter()
-            .enumerate()
-            .map(|(i, a)| if multi(i, a) { Arg { value: Value::Error(CellError::Value), from_ref: false } } else { a.clone() })
-            .collect(),
-    )
+    Some(args.iter().enumerate().map(|(i, a)| if multi(i, a) { Arg::val(Value::Error(CellError::Value)) } else { a.clone() }).collect())
 }
 
 /// Lookups whose every call searches a lookup vector from its start, so a call lifted over `n`
diff --git a/crates/functions/src/util.rs b/crates/functions/src/util.rs
index 14c627937..4e7853d2c 100644
--- a/crates/functions/src/util.rs
+++ b/crates/functions/src/util.rs
@@ -51,7 +51,7 @@ pub(crate) fn arg(args: &[Arg], i: usize) -> R<&Arg> {
 
 /// Whether argument `i` was supplied (present and not an empty literal like `F(1,)`).
 pub(crate) fn has(args: &[Arg], i: usize) -> bool {
-    matches!(args.get(i), Some(a) if !matches!(a.value, Value::Empty) || a.from_ref)
+    matches!(args.get(i), Some(a) if !matches!(a.value, Value::Empty) || a.from_ref || a.blank_value)
 }
 
 /// Number coercion for a scalar parameter: empty = 0, TRUE = 1, numeric text parses.